WO2006102388A1 - Conception de capteur tomographique en volume de capacitance electrique en temps reel et en 3d et reconstruction d'image - Google Patents

Conception de capteur tomographique en volume de capacitance electrique en temps reel et en 3d et reconstruction d'image Download PDF

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WO2006102388A1
WO2006102388A1 PCT/US2006/010352 US2006010352W WO2006102388A1 WO 2006102388 A1 WO2006102388 A1 WO 2006102388A1 US 2006010352 W US2006010352 W US 2006010352W WO 2006102388 A1 WO2006102388 A1 WO 2006102388A1
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dimensional
image
capacitance
image reconstruction
sensor
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Warsito Warsito
Qussai Marashdeh
Liang-Shih Fan
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The Ohio State University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
    • G06T11/003—Reconstruction from projections, e.g. tomography
    • G06T11/006—Inverse problem, transformation from projection-space into object-space, e.g. transform methods, back-projection, algebraic methods
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/05—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves 
    • A61B5/053—Measuring electrical impedance or conductance of a portion of the body
    • A61B5/0535—Impedance plethysmography
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N27/00—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means
    • G01N27/02—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance
    • G01N27/22—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance by investigating capacitance
    • G01N27/226—Construction of measuring vessels; Electrodes therefor
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
    • G01N33/15—Medicinal preparations ; Physical properties thereof, e.g. dissolubility
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
    • G01N33/24—Earth materials
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2211/00—Image generation
    • G06T2211/40—Computed tomography
    • G06T2211/412—Dynamic
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2211/00—Image generation
    • G06T2211/40—Computed tomography
    • G06T2211/424—Iterative
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2211/00—Image generation
    • G06T2211/40—Computed tomography
    • G06T2211/428—Real-time

Definitions

  • the present invention generally relates to process tomography and, in particular, relates a dynamic three-dimensional image electrical capacitance tomography.
  • the recent progress in the development of such measuring techniques as process tomography has provided more insights into complex multiphase flow phenomena in many industrial processes often in a combination gas, liquid and solid states, including pneumatic conveying, oil pipe lines, fluidized beds, bubble columns and many other chemical and biochemical processes.
  • the technique is capable of monitoring and control, both continuously and simultaneously, the local and global dynamic behavior of gas bubbles and solid particles in a non-invasive manner.
  • electrical tomography including capacitive, conductive or inductive modalities, is the most promising technical for dynamic flow imaging purpose.
  • the technique has a relative high temporal resolution, up to a few milliseconds, with sufficient spatial resolution, up to 1 to 3% of column diameter.
  • Tomography technique in general, generates a two-dimensional image called a "tomogram" (i.e., a two-dimensional (2D) image).
  • a three-dimensional image of an object is usually generated by stacking up the tomograms.
  • This is termed "static" three- dimensional (3D) imaging, because the 3D image could only be generated from a static or slow moving object. Therefore, this 3D imaging cannot be applied to situations with a fast moving object, or highly fluctuating multiphase flow media.
  • 3D imaging cannot be applied to situations with a fast moving object, or highly fluctuating multiphase flow media.
  • the tomogram is reconstructed from a capacitance sensor, which is in fact, geometrically three-dimensional.
  • slice imaging is not possible for ECT due to the extended length of the electrode.
  • the obtained 2D image is a result from projections of the object on a cross- section by assuming no variation in the axial direction. Therefore, the 2D ECT is actually unreal in the sense that the three-dimensional object needs to be assumed to have an infinite length. This is one of the major drawbacks of conventional ECT, and becomes problematic when the variation in the permittivity along the axial direction is significant.
  • electrical tomography either resistance or capacitance, has a potential for volumetric imaging, as electrical current or wave, spreads to three-dimensional space.
  • the "soft field" effect of the electrical field is once considered as one disadvantage of the technique for imaging applications, but it may advantageous to realize the volumetric imaging based on tomography technique.
  • electrical tomography is typically implemented based on measurements of a single constitutive property (i.e., permittivity for capacitance tomography, conductivity for resistive and impedance tomography and permability for induction tomography).
  • a single constitutive property i.e., permittivity for capacitance tomography, conductivity for resistive and impedance tomography and permability for induction tomography.
  • Multimodal tomography is generally implemented through three different strategies: (1) integration of two or more tomography hardware sensors into one imaging system ⁇ e.g., gamma-ray and ECT tomography), (2) use of reconstruction techniques capable of differentiating between different phases based on the same sensing signal ⁇ e.g., NN-MOIRT), and (3) use of the same sensor hardware to acquire different signals corresponding to different electrical properties (impendence tomography sensors for imaging permittivity and conductivity).
  • the first strategy is fast, it has the major disadvantage in terms of its high cost and complexity (added hardware).
  • the data acquisition needs to be carefully coordinated to yield consistent data at different given time frames for real-time applications.
  • the second strategy is the least costly to implement.
  • the third strategy is inherently multi-modal since it provides all the required information (on the different electrical properties) using the same sensor hardware and same reconstruction technique.
  • integration of such systems with multi-modal reconstruction techniques can provide independent data for different phases in the imaging domain. For example, obtaining both capacitive and conductive (impedance) flow information simultaneously is beneficial in many applications. This is particularly true when the flow under consideration is a mixture of phases with widely different conductivity and permittivity constants, such as oil flow in a pipeline.
  • EIT Electrical impedance tomography
  • ECVT electrical capacitance volume-tomography
  • This technique generates, from the measured capacitance, a whole volume image of the region enclosed by a geometrically three-dimensional capacitance sensor.
  • the principle components of this technique includes a three-dimensional capacitance sensor, data acquisition electronics and an image reconstruction algorithm which enables the volume-image reconstruction.
  • a new non-invasive multimodal tomography system based on the use of ECT sensor technology. Unlike usual ECT sensor operation that assumes a static interrogating field, the interrogating field of the system operates under quasi-static conditions.
  • the sensor is used to simultaneously measure variations in both capacitance and power corresponding to permittivity and conductivity distribution, respectively, within the sensing domain, or vessel.
  • a dual capacitance/power sensivity matrix is obtained and used in the image reconstruction algorithm.
  • dynamic three-dimensional image electrical capacitance tomography sensor system is disclosed.
  • the technique generates, from the measured capacitance, a whole volume image of the region enclosed by the a geometrically three-dimensional capacitance sensor.
  • a real time, three-dimensional imaging of a moving object or a real time volume imaging ⁇ i.e., four-dimensional (4D)) allows for a total interrogation scheme of the whole volume within the domain of an arbitrary shape of geometry to be implemented.
  • the system comprises a three-dimensional capacitance sensor, data acquisition electronics and the image reconstruction algorithm which enables the volume-image reconstruction.
  • the electrode shape of the capacitance sensor can be rectangular, triangular, trapezium, or any shape that encloses a three- dimensional section of the measuring domain and that distributes the electrical field intensity in three directions with equal sensitivity strength or comparable sensitivity strength.
  • the image reconstruction algorithm reconstructs simultaneously the image voxels in a three-dimensional array.
  • the tomography sensor system may also be multimodal. hi accordance with embodiment of the present invention, ECVT is also applicable for 3D medical imaging of the human body.
  • ECVT is also feasible for real time imaging of multiphase flow systems.
  • ECVT is also feasible interrogation of the whole vessel or conduit with an arbitrary shape of geometry. Accordingly, it is a feature of the embodiments of the present invention to produce real time three-dimensional imaging of a moving object, or real time four-dimensional volume imaging.
  • Figs. IA-B illustrate possible sensor designs according to one embodiment of the present invention.
  • Figs. 1C illustrates volume image digitization according to one embodiment of the present invention.
  • Fig. 2 illustrates three-dimensional sensitivity maps according to one embodiment of the present invention.
  • Fig. 3 illustrates axial sensitivity distribution for all capacitance readings according to one embodiment of the present invention.
  • Fig. 4A illustrates reconstruction results for a sphere object using NN-MOIRT according to one embodiment of the present invention.
  • Fig. 4B illustrates reconstruction results for a sphere and one half of a sphere using NN-MOIRT according to one embodiment of the present invention.
  • Fig. 4C illustrates reconstruction results for a dielectric block using NN-MOIRT according to one embodiment of the present invention.
  • Fig. 5 illustrates reconstruction results for a sphere in the center and the edge of sensing domain using the LBP technique according to one embodiment of the present invention.
  • Fig. 6 illustrates reconstruction results for a sphere in the center and the edge of sensing domain using the Landweber technique according to one embodiment of the present invention.
  • Fig. 7 illustrates reconstruction results for a sphere in the center and the edge of sensing domain using NN-MOIRT according to one embodiment of the present invention.
  • Fig. 8 illustrates a 3D image of a falling sphere reconstructed using the Landweber technique according to one embodiment of the present invention.
  • Fig. 9 illustrates a 3D image of a falling sphere reconstructed using NN-MOIRT according to one embodiment of the present invention.
  • Fig. 10 illustrates snapshots of 3D volume images of gas-liquid flow in a bubble column according to one embodiment of the present invention.
  • Fig. 11 illustrates snapshots of volume image of bubble in gas-solid fluidized bed using group B particles according to one embodiment of the present invention.
  • Fig. 12 illustrates different electrode designs according to one embodiment of the present invention.
  • Fig. 13 illustrates different capacitance sensor designs for ECVT applications according to one embodiment of the present invention.
  • Fig. 14 illustrates reconstruction of the simulated data for the diffusion case in multimodal tomography according to one embodiment of the present invention.
  • Fig. 15 illustrates reconstruction of simulated data for the conviction case in multimodal tomography according to one embodiment of the present invention.
  • a technique to reconstruct simultaneously a volume image of a region inside a vessel from capacitance measurement data using capacitive sensor electrodes attached on the wall of the vessel is developed. Due to the "soft field” nature of the electrical field, the capacitance measurements can be made using arbitrary shapes of electrodes and vessels.
  • volume tomography instead of 3D tomography stems from the fact that the technique generates simultaneous information of the volumetric properties within the sensing region of the vessel with an arbitrary shape. The terminology is also chosen to differentiate the technique from a "static" 3D or quasi-3D tomography technique.
  • the development of the technique primarily includes the evalution of the capacitance tomography sensor design and volume image reconstruction algorithm. The tests on capacitance data set obtained from actual measurements are also shown to demonstrate the validity of the technique for real time, volume imaging of a moving object.
  • An ECT sensor generally consists of n electrodes placed around the region of interest, providing n(n - l)/2 independent mutual capacitance measurements used for image reconstruction. Unlike usual EIT sensors that use direct current injection as excitation signal, ECT sensors rely on a time varying driving signal for capacitance measurements.
  • Equations (2) and (3) relate the permittivity and conductivity distributions to the boundary measurements of capacitance and power, respectively.
  • the solutions of both equations given a ⁇ (x, y) and ⁇ (x, y) distribution constitutes the forward problem solution.
  • the process of obtaining ⁇ (x, y) and ⁇ (x, y) distributions from the boundary measurements is the inverse problem.
  • the electrical capacitance tomography involves tasks of collecting capacitance data from electrodes placed around the wall outside the vessel (forward problem) and reconstructing image based on the measured capacitance data (inverse problem).
  • Equation 4 The measured capacitance Q of the z'-th pair between the source and the detector electrodes is obtained by integrating Equation 4:
  • Equation 5 relates dielectric constant (permittivity) distribution, ⁇ (x,y,z), to the measured capacitance, Q.
  • linearization techniques provide accurate and relatively fast solutions, they are limited to very simple geometries with symmetric permittivity distributions, and are not applicable to industrial tomography systems with complex dynamic structures.
  • numerical methods can provide fairly accurate solutions for arbitrary property distributions. They, however, consume excessive computational time which is impractical for tomography application with iterative image reconstruction.
  • linearization methods provide relatively fast and simple solution, though they show a smoothing effect on a sharp boundary of the reconstructed image. The smoothing effect is improved with iteration in the image reconstruction process.
  • Equation 6 Equation 6
  • sensitivity The integration part divided by the voltage difference is called as sensitivity, which can be derived as:
  • Equation 5 can then written in matrix expression as:
  • C is the M-dimension capacitance data vector
  • G is N-dimension image vector
  • N is the number of voxels in the three-dimensional image
  • M is the number of electrode- pair combinations.
  • N is equal to nxnxriu where n is the number of voxel in one side of image frame (layer); H L is the number of layers.
  • the sensitivity matrix S has a dimension of MXN.
  • the Inverse Problem The image reconstruction process is an inverse problem involving the estimation of the permittivity distribution from the measured capacitance data. In Equation 9, if the inverse of S exists, the image can be easily calculated.
  • the iterative image reconstruction process involves finding methods for estimating the image vector G from the measurement vector C and to minimize the error between the estimated and the measured capacitance, under certain conditions (critera), such that:
  • Landweber technique also called iterative linear back projection (ILBP), which is a variance of a steepest gradient descent technique commonly used in optimization theory.
  • ILBP iterative linear back projection
  • Equation 12 The iteration procedure based on the steepest gradient descent technique becomes Equation 12.
  • the capacitance difference ⁇ C becomes insignificant, and the image is iteratively corrected by the sensitivity S ⁇ , producing the so-called "sensitivity-caused artifacts.” As a consequence, the generated image seems to be directed toward the stronger side of sensitivity.
  • a multi-criterion optimization based image reconstruction technique for solving the inverse problem of 2D ECT is extended to solve the inverse problem of the 3D ECT.
  • the optimization problem finds the image vector that minimizes simultaneously the four objective functions: negative entropy function, least square errors, smoothness and small peakedness function, and 3-to-2D matching function.
  • all the other functions involved in the reconstruction process collectively define the nature of the desired image based on the analysis of the reconstructed image.
  • the error which is generated from the linearized forward solver and propagated to the reconstructed image through the least square objective function, is minimized with the other objective functions applied.
  • the negative entropy function, which should be minimized is defined as in Equation 13:
  • Equation 14 The least weighted square error of the capacitance measurement is defined in Equation 14: where S is the 3D sensitivity matrix with dimension of M by N, and Mis the corresponding number of the measured capacitance data. ⁇ 2 is normalized constant between 0 and 1.
  • the smoothness and small peakedness function is defined as in Equation 15:
  • Equation 16 An additional objective function for the 3D image reconstruction is required to match the 3D reconstructed image to the 2D, namely 3-to-2D matching function, which is defined in Equation 16 as:
  • H 2D is projection matrix from 3D to 2D, having dimensions of NxN2D- N ZD is the number of voxels in one layer of the 3D volume image vector G.
  • ⁇ 4 is a constant between 0 and 1.
  • the 2D image vector is the 2D solution of the inverse problem in the image reconstruction.
  • the multi-criteria optimization for the reconstruction problem is to choose an image vector for which the value of the multi-objective functions are minimized simultaneously.
  • Hopf ⁇ eld and Tank proposed a technique based on a neural network model to solve optimization problem and in particular they presented a mapping of the traveling salesman problem onto neural networks. Since then, Hopfield neural networks model (or simply called Hopfield nets) has been used to successfully address a number of difficult optimization problems, including image restoration and image reconstruction for "hard field” tomography and “soft field” tomography. Their advantages over more traditional optimization techniques lie in their potential for rapid computational power when implemented in electrical hardware and inherent parallelism of the network.
  • the image voxel value Gj to be reconstructed is mapped into the neural output variable v j in the Hopfield nets.
  • the output variable is a continuous and monotonic increasing function of the internal state of the neuron u j as shown in Equation 17:
  • ⁇ is a steepness gain factor that determines the vertical slope and the horizontal spread of the sigmoid-shape function.
  • the behavior of a neuron in the network is characterized by the time evolution of the neuron state U j governed by the following differential Equation 19:
  • Equation 20 The time constant of the evolution is defined by Equation 20:
  • Equation 21 E ⁇ G) (G)dG (21)
  • Equation 21 The first term in Equation 21 is the interactive energy among neurons based on the objective functions described above.
  • the second term is related to the violation constraints (penalty functions) to the three weighted square error functions which must also be minimized.
  • the third term encourages the network to operate in the interior of the N- dimensional unit cube (0 ⁇ G j ⁇ 1) that forms the state space of the system.
  • N is the number of neurons in the Hopfield nets, which is equal to the number of voxels in the digitized volume image.
  • Equation 22 Equation 22
  • Equation 23 Equation 23:
  • Equation 23 can be solved, for example, using Euler's method to obtain time evolution of the network energy.
  • the form of penalty parameter ⁇ k is chosen as Equation 24:
  • the penalty parameter provides a mechanism for escaping local minima by varying the direction of motion of the neurons in such a way that the ascent step is taken largely by the penalty function in the initial steps.
  • W 1 [w n ,w l2 ,A,w, N ] T ;
  • G 2D (t ⁇ ) [G 2D ⁇ (t ⁇ ), G 2D ⁇ 2 (t ⁇ ), ⁇ , G 2DtN2D (t ⁇ )f
  • the neuron output corresponds to the voxel value is updated as Equation 26:
  • the first step is preprocessing by solving the 2D image matrices in Equation 16 using ⁇ -MOIRT.
  • the steepness gain factor ⁇ is set to 2.
  • the initial weights are
  • ⁇ 0) [ ⁇ G ⁇ (0)XG(0) + ⁇ G ⁇ (O)G(O)]- 1 ,
  • the image reconstruction procedure is stopped when the termination scalar is determined to be G. (t + At) - G j (Of ⁇ 10 "4 for all neurons (voxels).
  • the sensitivity matrix In two-dimensional ECT, the sensitivity matrix only has variation in radial ⁇ i.e., x- and y-axes) directions, assuming infinite length of the electrode in the z-direction. Imaging a three-dimensional object requires a sensitivity matrix with three-dimensional variation, especially in the axial (z-axis) direction to differentiate the depth along the sensor length. Therefore, the fundamental concept of the electrical capacitance sensor design for the 3D volume imaging is to distribute equally the electrical field intensity (sensitivity) all over the three-dimensional space (control volume) or with comparable electrical field intensity strength. This concept relates to the sensitivity variance (the difference between the maxima and minima) and the sensitivity strength (the absolute magnitude).
  • the triangular sensor in Fig Ia comprises a triangular shape 1 electrode that forms six panels of two sensors 7 and 8.
  • the choice of the electrode number is based on the data acquisition system available which has 12 channels. However, the use of any other number of electrodes is possible.
  • different shaped sensors such as trapezoidal or any other shape or combination of different shapes, to enclose the 3D sensor region are also feasible as long as the sensor provides three-dimensional sensitivity distribution with relatively equal order of sensitivity strength or with comparable sensitivity strength.
  • the electrodes are arranged in three planes where each plane is shifted to another to distribute the electrical field intensity more uniformly in the axial direction and to increase the radial resolution up to twice the radial resolution of a 4-electrode sensor.
  • the radial resolution of the rectangular sensor with this electrode arrangement thus equals 8-electrode sensor per plane.
  • the number of planes also can be greater than two to provide better variation in the axial direction.
  • trapezoidal, triangular or any non-rectangular geometric shape sensors it is also possible to use just a single plane.
  • the sensitivity maps of the two capacitance sensors are illustrated in Fig. 2.
  • the sensitivity maps show distributions of sensitivity variation in three-dimensional space.
  • the sensitivity maps of capacitance readings between any electrode pair have a three-dimensional variation.
  • the maps show relatively comparable axial and radial sensitivity variation for the rectangular sensor, but less equally for the triangular sensor. Equal sensitivity variation all over the sensing domain is essential to avoid an artifact or image distortion in the reconstruction result due to inequality in the sensitivity strength distribution.
  • the largest magnitude in the sensitivity is found in the same-plane electrode pair capacitance reading, while the lowest is in the electrode pair between the first and third layers.
  • the magnitude of the sensitivity strength does not affect significantly the image reconstruction process but it relates largely to the Signal-to-Noise Ratio (SNR) in the capacitance measurement.
  • SNR Signal-to-Noise Ratio
  • the sensitivity strength in the first and third layers of electrode pairs is one order less in magnitude than that of the same-plane electrode pair. Therefore, the capacitance measurement between the first and third planes is very sensitive to noise. Therefore, the sensor requires very careful manufacture.
  • the capacitance measurement between inter-plane electrode pair is related mostly to the horizontal length of the rectangular electrode, and is almost independent of the axial length of the electrode.
  • a dual sensitivity matrix (capacitance plus power measurement data) can be constructed and used for solving both forward and inverse problems.
  • the dual matrix elements are approximated based on the electric field distribution in the empty sensor scenario.
  • the difference in capacitance is related directly to the difference in total stored energy caused by the permittivity pixel.
  • This energy difference is composed of two components: internal to the pixel ⁇ Wj nt and external to the pixel ⁇ W ext .
  • the constants ⁇ j nt and ⁇ ext are introduced to simplify the final equations. Combining both energy components, we have:
  • the capacitance difference introduced by a small perturbation in permittivity is proportional to the square of the unperturbed electric field (empty vessel).
  • the sensor model has to be solved once in the empty case.
  • each element in the power matrix linearizes the relation between the conductive (heating) loss and a small conductive pixel perturbation in an insulating background given by 3, integrated over the (small) pixel volume having conductivity. Based on these results, the power sensitivity matrix elements are approximated as follows:
  • the dissipated power inside the pixel is calculated based on the electric field in the empty sensor case.
  • the same field solution used for calculating the capacitance sensitivity matrix can be used here for calculating the power sensitivity matrix.
  • a 12-channel data acquisition system (DAM200-TP-G, PTL Company, UK) can be used.
  • the ECT system comprises a capacitance sensor, sensing electronics for data acquisition and a processing system for image reconstruction.
  • the sensors can include two types of 12-electrode systems as illustrated in Fig. 1.
  • the length of the sensing domain of the capacitance sensor can be about 10 cm with a column diameter of about 10 cm.
  • the data acquisition system can be capable of capturing image data up to about 80 frames per second.
  • the image is reconstructed on a 20x20x20 resolution based on the algorithm described above.
  • the volume image digitization is illustrated in Fig. Ic.
  • An ECT sensor was used to assess the multimodal tomography system performance.
  • the sensor operates at about 10 MHz.
  • Simulations for sensitivity calculations and boundary measurements can be carried out using FEM.
  • a dual sensitivity matrix for capacitance and power perturbations was constructed based on the electric field solution of the sensor in its empty state.
  • the reconstruction process, data forward simulations, and data post-processing can be processed on a Pentium IV computer, with a 3 GHZ processor and with a 3 GB RAM memory.
  • Fig. 4 illustrates the three-dimensional reconstruction results of a dielectric sphere, a one and half sphere and a dielectric block based on simulated capacitance data using NN-MOIRT algorithms.
  • the diameters of both spheres are half the diameter of the sensor equaling the whole dimension of the image.
  • the sensor used was a 12-electrode twin- plane triangular sensor. Excellent agreements between the reconstructed 3D images and the model images were obtains for all images.
  • the reconstruction results from measurement data are shown in Figs. 5-7 using the two electrode designs illustrated in Fig. 1 and the three reconstruction algorithms: LBP, Landweber (or ILBP), and NN-MOIRT.
  • the iteration number was set to 100 in all cases.
  • the reconstructions are based on actual capacitance measurements of dielectric objects: one sphere located in the center of the sensing domain and another sphere located half inside the sensing domain.
  • Each row in every figure contains two slice images of X-Z and Y-Z cuts in the first two columns and one 3D image in the third column.
  • the 3D image can be an isosurface display with an isovalue of half of the maximum permittivity.
  • Fig. 5 illustrates the reconstruction results on the LBP technique. Elongation in axial direction of the reconstructed images occurs to both the objects for the single-plane triangular sensor.
  • the axial elongation effect is expected as the sensitivity variation in the axial direction for the triangular electrode is insignificant as compared to that in the radial direction (see Fig. 3a).
  • the technique gives relatively accurate shapes of the objects through a smoothing effect appears in the sharp boundary of the reconstructed images.
  • the contrasts between low and high permittivity regions in the reconstructed images are relatively uniform in both radial and axial direction.
  • Fig. 6 illustrates the reconstruction results for the Landweber technique (or iterative LBP). The reconstructed images are severely distored in all cases for both sensor designs. An elongation effect is also observed for the triangular sensor.
  • the reconstructed images appear to be directed toward the sensing sites with relatively stronger sensitivities, which correspond to the junctions between electrodes, causing a distortion and elongation due to a "sensitivity-caused artifact" as described above.
  • the distortion may also arise from noises contained in the capacitance data.
  • Fig. 7 The reconstructed volume images using the NN-MOIRT algorithm are illustrated in Fig. 7.
  • the triangular sensor although the elongation effect is still observed, the results are much better compared to those using LBP and Landweber techniques.
  • the effect of noise to the reconstructed image is also minimal as compared to the Landweber technique.
  • the reconstructed images are almost perfect except for the contrast which is less clear as compared to the triangular sensor.
  • Figs. 8 and 9 show a series of instantaneous volume-image of the same dielectric sphere used in Fig. 5-7 when falling through the inside of the sensor based on image reconstruction results using the Landweber technique and NN-MOIRT. A distortion in the shape of the reconstructed images from level to level is observed in the Landweber technique results.
  • the shape of the reconstructed images using NN- MOIRT is relatively conserved at every level, verifying the capability of the algorithm to resolve, to some extent, the effect of "sensitivity-cause artifact.”
  • This result also indicates that the technique requires fewer measurement data to generate the same image quality as produced by the Landweber technique.
  • the capability to minimize the effect of "sensivity- caused artifact” is essential, in particular for volume imaging, as there will always be non- uniformity in the sensitivity strength due to the 'soft field” effect.
  • the use of entropy function and the distribution of the weight coefficients to the different objective functions are considered to be effective in minimizing the effect of "sensitivity-caused artifact.” Both factors are unique to the NN-MOIRT algorithm.
  • Distribution of weight coefficients is made in such a way to provide a uniform speed of convergence in each voxel.
  • FIG. 10 which shows a snapshot of the tomography volume image (3D gas concentration distribution) of the multiphase flow.
  • the tomography volume image is constructed from permittivity voxel values in 4D matrix components, i.e., three space components with spatial resolution of 5x5x8 mm 3 and one time component with a temporal resolution of 12.5 ms.
  • the voxel permittivity values are converted into phase concentration (holdup) of the multiphase system based on the capacitance model described above.
  • the first two figures in the top row are slice cut images of the planes defined by the coordinate system in the bottom-right in the figure.
  • the first and second figures in the bottom row are, respectively, a 3D volume image which is partly cut-off to display the inside of the 3D representation and a 3D isosurface image which displays the 3D boundary (surface) of the bubble swarm image.
  • the cut-off boundary value was set at 10% of the gas holdup value.
  • the cut-ff boundary selection was arbitrary and used to provide some sense of distinction of the boundary of high- concentration bubble swarm from the surrounding low gas concentration region.
  • a photograph of the two-phase flow was taken using a high-speed digital video camera under the same conditions is displayed on the right-hand side of the figure.
  • An example of the application result of the technique for multiphase flow imaging of gas-solid flow in a vertical column is illustrated in Fig. 11, showing a well-known apple shape image of a bubble in gas-solid fluidization system as compared with a ID X-ray photograph.
  • the image confirms the accuracy and quickness in real-time volume-imaging of moving dielectric objects.
  • Figs 12 (a-c) illustrate different designs of capacitance electrodes selected based on different shapes of control volume and imaging purposes.
  • the technique is feasible for volume imaging of multiphase systems in conduits such as pipe bends, T- junctions, conical vessels or other complex geometrical systems shown in Fig. 13.
  • the technique is open possible for real time 3D medical imaging of the human body as well as for the real time monitoring of tablet manufacturing in the pharmaceutical industry.
  • the "soft field" nature and ill-posedness of the inverse problem are the main problems encountered in the reconstruction process.
  • Iterative linear back projection (ILBP) is used for image reconstruction for the multimodal tomography system. In ILBP, both forward and inverse problems are solved iteratively to minimize the residual image error.
  • ILBP Iterative linear back projection
  • a dual modality sensitivity matrix is used here.
  • the first component of the matrix represents the capacitance perturbation, whereas the second component refers to the conductivity perturbation.
  • the image vector is updated iteratively to minimize the error between measured and calculated integral measurement data according to:
  • G k+ ' G k + ⁇ (s ⁇ (M- SG k )) OD
  • the calculated boundary value is obtained from the reconstructed image using linear forward projection.
  • G is the image vector
  • k is the iteration number
  • S is the sensitivity matrix
  • r is a factor controlling reconstruction convergence
  • M is the boundary measurement.
  • Fig. 14 and 15 Reconstruction results for diffusion- and convection-dominated cases are presented in Fig. 14 and 15 respectively.
  • the high value of conductivity constant in the center region enables the solution to converge to two distinct regions of permittivity and (pure) conductivity maps.
  • the electrical field distribution is mainly controlled by the permittivity constant due to relatively small values of conductivity.
  • the permittivity reconstruction captures both the center and ring distributions.
  • the conductivity reconstruction is able to reconstruct the center conductive region satisfactorily.
  • an independent reconstruction of permittivity and conductivity can be implemented.

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Abstract

La présente invention concerne un système de capteur tomographique de capacitance électrique d'imagerie dynamique à trois dimensions. Selon cette invention, une image en volume globale de la région entourée par le capteur de capacitance à trois dimensions géométriques est produite à partir de la capacitance mesurée. Une imagerie à trois dimensions en temps réel d'un objet en mouvement ou une imagerie en volume en temps réel (c'est-à-dire à quatre dimensions (4D)) permet de mettre en oeuvre un schéma d'interrogation total de tout le volume à l'intérieur du domaine d'une forme géométrique arbitraire. Le système comprend un capteur de capacitance à trois dimensions, un système électronique d'acquisition de données et l'algorithme de reconstruction d'image qui permet la reconstruction de l'image en volume. La forme d'électrode du capteur de capacitance peut être rectangulaire, triangulaire, trapézoïdale ou n'importe quelle forme englobant une section à trois dimensions du domaine de mesure ou distribuant l'intensité de champ électrique dans trois directions avec une même sensibilité. L'algorithme de reconstruction d'image reconstruit simultanément les voxels d'image dans un réseau à trois dimensions. Le système de capteur tomographique peut être multimodal.
PCT/US2006/010352 2005-03-22 2006-03-22 Conception de capteur tomographique en volume de capacitance electrique en temps reel et en 3d et reconstruction d'image WO2006102388A1 (fr)

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